The invention relates to an eccentric grinder. More particularly it relates to an eccentric grinder which has an eccentrically circulating grinding disc with a gear rim rolling on another gear ring. Such an eccentric grinder is disclosed in DE PS 36 25 655. In the very fine grinding stage, this grinder is safe-guarded against an undesirable increase of the rotary speed of the grinding disc to the idling speed of the machine. This safeguard has been designed in the form of a friction brake, which however requires a considerable number of individual parts and elaborate assembly work. The friction brake is prone to problems and is sensitive to dust. A major effort in sealing technology has therefore to be made. The reliability of the brake diminishes as the wear of its individual parts, such as springs and brake linings, increases. Their repair requires substantial costs. In the harsh industrial operating environment, the known eccentric grinder has the following further disadvantages: The teeth of the eccentric gear are subject to high wear due to the effect of grinding dust. The change-over gear for the additional grinding stage for producing a medium coarseness requires complicated means of setting, which are susceptible to trouble and are lacking in stability. Any careless operation of the gear changes poses the risk of breaking the eccentric gear teeth.